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“Give me a coin. <Takes Coin.> All right. Uh… heads, I win, tails, you lose. Right? <Flips coin.> Tails, you lose.” -Ralph Kramden
All things being equal, you’re well aware that if you flipped a completely fair coin, you’d have a 50% chance of it landing on heads, and a 50% chance of landing on tails (ignoring the side, of course).
Image credit: C. Nolan, A. Eckhart and Warner Bros. Pictures, retrieved from http://explow.com/Two-Face.
So let’s imagine that you flip the coin ten times, and you get seven heads and three tails. Are you worried? You shouldn’t be; in order to tell whether a coin is biased or not, you need to build up the proper statistics to actually tell. Flipping a coin ten times, your probability of getting exactly five heads and five tails is pretty small: only about 25%.
So let’s say, now, that I do have a biased coin, but it’s only slightly biased. Let’s say it’s biased by just 1%, so that 50.5% of the time, I’d get heads, and 49.5% of the time, I’d get tails. How many flips would I conclusively need to determine whether the coin is biased or not?
Image credit: Anthony Watts, who makes proper use of the gnu rand() function.
Believe it or not, the answer is somewhere around 250,000! A fair coin flipped a little less than that — ten-thousand times, shown above — has about a 32% chance of showing a 1% bias or greater in either direction. If you flipped a coin 10,000 times and got 5050 heads, that’s what we call a result with 1-sigma (1-σ) significance: something we’re not very confident in.
But if there was a 5% bias, if we got 5250 heads in 10,000 flips, that’s a very rare occurrence with a fair coin: a result that far off from the expected value of 5000 heads happens only 0.00006% of the time (a 5-σ result) with a truly fair coin. If that was our result, we’d be highly suspicious, and rightfully so, that something was amiss with the coin. We can get that same level of significance for a coin with a 1% bias, but every time you halve the size of the effect, you need to quadruple how much data you take in order to observe it. A coin that was biased by just 0.01% would take more than two billion flips before you could conclude with confidence that it was, in fact, biased.
Image credit: Harrison Prosper at Florida State University.
Now, in particle physics, we don’t have heads-and-tails that tell us what we’re going to get out when we collide things together; we have the standard model, whose particles are shown above. All of the quarks, leptons, and gluons have been discovered and confirmed, as has the photon and the three weak bosons. The only one not yet discovered is the Higgs.
Image credit: CERN / ATLAS / LHC outreach.
So, here’s the deal. We know — when we smack any two particles together at any given energy — we know, based on all the known particles and their properties, how frequently we ought to see all the different types of events that can occur in nature.
So what we do is we compute what the probability of having each type of result is with all the known particles (i.e., without the Higgs), then we do our collisions, record the data, and compare what we get with what we think we should get. The first machine to really get into this game and put something significant out was the Large Hadron Collider (LHC), which released its preliminary results late last year.
Image credit: CERN / Particle Physics for Scottish Schools.
How does this work? There are two beams at very high energies rotating and accelerated in opposite directions (clockwise and counter-clockwise), and then squeezed together into a couple of different collision points. The two largest, most sophisticated particle detectors ever built — CMS and ATLAS — are centered right around these collision points, poised to observe in gory detail the particle shrapnel that comes out of these miniature fireworks.
Image credit: © 2012 The School of Physics and Astronomy, The University of Edinburgh.
And there are plenty of fireworks that come out of every collision. The reason we need that ultra-sophisticated detector is because we want to reconstruct, to the best of our ability, exactly what it was that was created in that collision, with what momentum it was created, and where it originated. Given the complexity of what comes out, it’s remarkable that we can do it at all.
Image credit: Julian Bunn/CERN and Harvey Newman/Caltech.
Last year’s preliminary results from both CMS and ATLAS showed hints of a new particle that would be consistent with a Higgs, but not quite at a significance required to claim discovery.
Image credit: CERN / Guido Tonelli, for the CMS collaboration.
As you can see, CMS’s results, above, show a significant excess over what’s expected at an energy of about 125 GeV. The significance is only around 3-σ, not the 5-σ “gold standard” that’s required for discovery. But if this is real, we should see something very similar from the other detector, ATLAS. If we can’t confirm it with an independent experiment, that’s a big indication there’s a flaw. (Hi, OPERA!) But when we looked at the ATLAS results, below, we saw that there was no flaw.
Image credit: Fabiola Gianotti for the ATLAS collaboration / CERN.
Not only did ATLAS confirm what CMS saw — the same type of signal in the same spot — they saw it at an even higher statistical significance! Combined, the results from those two experiments could get up to alllllmost 4-σ, edging close to what we could finally call a discovery.
But not quite; we needed more data.
Image credit: the Tevatron at Fermilab, http://www.fnal.gov/.
The Tevatron at Fermilab, above, which was the previous record-holder for most powerful and sophisticated particle accelerator in the world, just released the full, final results from their cumulative data runs, attempting to find the Higgs. What did over a decade’s worth of high-energy data (but at significantly lower energy than the LHC) have to show?
Image credit: the Tevatron New Physics and Higgs Working Group, Fermilab.
As you can see, the blue curves, above, show what the Higgs-less, known standard model background ought to look like. The black points show what the Tevatron has actually observed, and the theoretical Higgs signal — that tiny extra bit — is shown in red. When all the data across all the energies is looked at together, we can construct a graph that shows us where there’s likely to be a Higgs, if anywhere, based on the data Fermilab has taken.
The final results?
Image credit: the Tevatron New Physics and Higgs Working Group, Fermilab.
Looks like it’s totally consistent with what CMS and ATLAS have observed, preliminarily. The confidence level isn’t great — again, only about a 3-σ significance — but it wasn’t released because it “proves” the Higgs.
It was released because tomorrow — July 4th — CERN is set to make a big announcement about the Higgs. And, like everyone else, you know what to expect.
Image credit: Hitchhiker's Guide to the Galaxy.
They’re very likely going to announce that the 5-σ threshold, the “gold standard” for discovery, has been reached, and that we’ve discovered the Higgs boson. The only question is whether CMS and/or ATLAS will have enough proverbial coin-flips to announce a discovery on their own (there’s a reason it’s taken this long), or whether they’ll need to combine results to reach that pinnacle. (My money’s on the former, which is more convincing, but we’ll have to wait and see.)
Assuming things go as we expect, the speculation will turn to the question of what does it mean, and I’ve got some early analysis for you.
Image credit: Fermilab’s “Higgs Missing Report,” 125 GeV bar by me.
For a Higgs right around 125 GeV, which is where all preliminary analysis points, we expect that the Higgs will be produced at a certain rate, and that it will decay into various other particles at particular rates. What are those rates? There’s an excellent analysis in this paper, that shows what the standard model rate is for various possibilities, and what the preliminary data is for each detector, thus far.
Image credit: P. P. Giardino et al., 2012.
If this is, in fact, where the Higgs appears to be, and the rates observed are consistent with the standard model predictions, and there are no other “new particle” announcements that come out on the 4th, then this is an amazing victory for the standard model.
And a nightmare scenario for everything else, including supersymmetry, extra dimensions, and string theory.
Image credit: DESY in Hamburg.
Because finding the standard model Higgs at this energy means that there’s no need for any of those things. A Higgs at 125 GeV and nothing else at the LHC, totally consistent with the standard model, mean that if supersymmetry exists, it needs to be at such a high energy that it no longer solves the problem it was designed to solve! Despite the absurd claims that others have made, this incredible standard model victory could finally start hammering nails into the coffin of low-energy supersymmetry, which was the prime experimental motivator for string theory in the first place.
So what do I predict we’re going to see?
Image credit: P. P. Giardino et al., 2012.
People examining very closely at the individual decay channels of the Higgs, searching for (not yet statistically significant) departures from what the standard model predicts, hoping for the new, beyond-the-standard-model physics that we all hope exists.
But based both on what we’ve seen so far and what I expect to see tomorrow, I just don’t think it’s in the data. I’m predicting total victory for the standard model, the most successful theory of all-time. I’ll have an update for you if anything new and surprising comes out — especially if it means something different than what I’ve written here — but for real-time news, faster than I can write it, I highly recommend visiting the Particle Physics trap at trap!t that I’ve built for us.
Happy 4th of July, and here’s hoping we can all enjoy the release of the greatest firework of them all.
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